Sunday, May 10, 2015

How to remember numerals better

In all the debate around "Whorfian" effects of language on cognition, one relatively well-known case has received oddly little attention among linguists, despite being widely discussed by psychologists and popularised by Malcolm Gladwell: the effect of word length on short-term memory (Baddeley et al. 1975). Basically, all other things being equal, it's easier to remember a sequence of short words than a sequence of long words. This suggests that our short-term memory for words (what psychologists confusingly call phonological memory) has a capacity limited by length - specifically, the amount that can be pronounced in about 2 seconds (Schweickert & Boruff 1987). That should suggest, in particular, that numbers presented orally will be easier to remember in a language with short numerals than in one with long numerals. (Note that this affects, among other things, IQ test results, since IQ tests typically include tests of numeral recall.)

Psychologists followed up on this by attempting to test this hypothesis with a number of language pairs (for an overview, see Baddeley (1997). Disclaimer: I'm not a psycholinguist, and the following references are certainly not exhaustive). The best-tested and most consistent result concerns Chinese. Mandarin and Cantonese numerals take shorter to say than English ones, and a number of psychologists have accordingly confirmed that Chinese speakers can remember longer numerals than English speakers (Stigler, Lee, & Stevenson (1986), Hoosain & Salili (1987)), even at 4 years old Chen and Stevenson (1988)), and that this applies even when bilinguals are tested across their two languages (Hoosain 1979). It goes further than that, in fact: Chincotta & Underwood (1997) find that, out of Cantonese, English, Greek, Finnish, Swedish, and Spanish, only Cantonese speakers remember significantly more digits than speakers of other languages - and that this difference disappeared if the subjects were prevented from rehearsing the numbers auditorily by being asked to keep repeating "la-la" while being tested, proving its linguistic nature. The difference ranges around 2 digits, with the exact figure depending on the experiment.

Data for other languages is less clearcut. Welsh numerals take longer to say in isolation than English ones, and Ellis & Hennelly (1986) accordingly found that English-Welsh bilinguals can on average remember longer numerals in English than Welsh. Naveh-Benjamin & Ayres (1986) simultaneously tested the hypothesis for university students in Israel speaking English, Spanish, Arabic, and Hebrew natively (but excluding the digits "seven" and "zero"). They found that the average number of digits recalled was highest in English (7.21), followed by Hebrew (6.51), then Spanish (6.37), and lowest in Arabic (5.77); the ordering by average number of syllables per digit, or by average time taken to read a digit, was English, Spanish, Hebrew, Arabic. However, the difference in number of digits recalled was smaller than predicted by the time taken to read a digit in each language, suggesting that other factors were also relevant.

A proviso is necessary: some recent work, without disputing the differences observed, has made a strong case that they relate not simply to length ( Lovatt, Avons, & Masterson 2000), but crucially to phonological factors (Service 2010, Lethbridge, Hinton & Nimmo 2002). This has been argued for Welsh numerals vs. English ones by Murray & Jones (2002), who find that Welsh digits take longer to say in isolation but actually take less time to say in connnected speech than English ones, and that changes of place of articulation at word boundaries negatively affect memory.

The research is curiously selective in terms of languages examined, and many of the experiments don't control for all possible confounding factors, such as diglossia and social status in the case of Welsh or Arabic. Nevertheless, it does at least seem well-established that speaking Chinese gives a short-term digit memory advantage over speaking major European or Semitic languages. So, if for some reason you regularly need to remember long numerals, and your preferred language doesn't happen to be Chinese, how do you compensate for this handicap?

There are two obvious ways to get around this (assuming you care enough about remembering numerals to want to, which depends very much on your tastes and circumstances). One is to remember the number visually (as a sequence of written digits) or even kinesthetically (as a sequence of typing actions), in which case this particular constraint no longer applies (cf. eg Olsthoorn, Andriga, & Hulstijn 2012). This only helps, however, if you remember numerals better visually or kinesthetically than auditorily, and my impression is that most people don't.

A probably more helpful alternative is to establish a code that lets you turn long numerals into much shorter words by identifying digits with single letters or single phonemes. This solution has a very long history in Arabic and Hebrew, in which each letter of the alphabet can be used to represent a digit: 'a is 1, b is 2, etc. (the first 9 digits are units, the second 10 are tens, and the rest are hundreds). Since short vowels are not letters, the resulting word can be given whatever vowels the user sees fit to give it. A common game of later poets using the Arabic script was to encode the date of their poem within the poem as a chronogram; more practically, Moroccan schoolchildren used to memorise the multiplication tables as a series of meaningless words formed by this encoding (Meakin 1905). Chronograms have been formed using Roman numerals, but for memorisation, at least, they are rather ill-adapted to such a system - think how much padding would be required to turn a number like MDCCCLXXXIII into words.

However, the spread of Hebrew studies in Western Europe following the Renaissance, and the increasing importance of memorising statistics there, encouraged European mnemonists to look for ways of emulating this encoding without having to learn a Semitic language. Doing so at a time when place notation was widely used, they introduced a crucial improvement: each consonant represented a digit in a place notation system, rather than a number in an additive notation system. After various cumulative efforts at improvement, this culminated in the early 19th century with the so-called Major system: 0=s/z, 1=t/d, 2=n, 3=m, 4=r, 5=l, 6=š/ž/č/j, 7=k/g, 8=f/v, 9=p/b, with vowels, semivowels, and laryngeals ignored. To remember 94801 (LACITO's zip code), for example, one would turn it into "professed". This system apparently remains in use among professional mnemonists to this day, despite being virtually unknown to wider society.

Perhaps this is why linguists haven't paid more attention to the word-length effect in the context of the Whorfian debate: it's a clear-cut effect of language on cognition, but not a very profound one, in that it should be fixable by some very simple hacks (or even just by borrowing some one else's numerals). But I'm not aware of any experimental work testing the effect of this particular hack on digit recall...

9 comments:

Fascinating stuff. I had a little song for remembering my Belgian bank account, but "septante-et-un" was crucial for the rhrythm, and "soixante-onze" would have thrown me absolutely.My magician (I'm sorry, I mean mathematician) friend had a three-digit number of which his bank account was (so he said) the third power. I'm in no position to contradict him.Who knows about any of this stuff?

Sorry to crash in, completely off-topic, but I have to spend two weeks in Oran in July. I can just about get by in Moroccan Darja, but my friend (born in Oran but completely francophone) tells me I should forget that altogether, and just speak French.Real questions coming up: How different can the Darja spoken in Ouijda and Oran really be? As a European, will I be taken REALLY badly in Algeria (Oran) as someone who talks like a Moroccan? Should I take my friend's advice, and stick to French?Sorry if these questions seem trivial, they're (pragmatically) quite important to me.

There is little difference between the Darja of Oran and Oujda, of course - avoid ka- and daba and people should barely even be able to tell. Even if they can tell I doubt they'd care, notwithstanding the two governments' best efforts to drive a wedge between their peoples.

How people will react to a European semi-speaker of Darja is another question, and one that I can't really help you with. Some people may appreciate it, but it will probably also make some people suspicious of you - this guy knows more Darja than an outsider should, but not enough Darja to be an insider. Context is also important - Darja may be acceptable at a corner shop but unacceptable from a foreigner in an airport or a posh restaurant. And traditional Algerian social norms weigh stronger when speaking Darja than when speaking French; so it helps if you know and respect those. Let me know how your language choices work out.

That's a really helpful reply, Lameen. Nisch the ka- and daba, I'll be monitoring myself for that. Of course, I was never contemplating initiating a conversation in Darja in Oran, just responding vaguely intelligently if it came up, and letting people know (as a kind of politeness) that I knew what they were talking about, in case they were tempted to talk behind my back to my face, as it were. Whether, in Morocco, I speak French/Spanish with a smattering of Darja words, or a kind of Arabic liberally sprinkled with French/Spanish words (Maltese?) is a matter for the sociolinguists.

On the little island where I was born (Jersey), any "foreigner" who speaks our dialect is regarded with enormous suspicion, and the better s/he speaks it, the greater the distrust. Of course, I could take (short-lived) pride in demonstrating that I speak better Arabic/Darja than my friend, but the Jewish and Christian Scriptures and the Koran all warn us against such a course, as though common sense weren't enough.

I might give my "Algerian" a little run-out with my friend's family, but at least publicly, it's better to stick to your "butin de guerre", French. You frighten me a little with your "traditional Algerian social norms". If that refers to forms of address, I'm criticized in Morocco for being "over-polite" (though it's much more complicated than French, I suppose that means roughly "vouvoyer"-ing people whom I ought to "tutoyer").

Here's a little off-off-topic question (but still about pronouns). Mon copain: "Ma soeur et sa copine sont allé au coiffeur et après ILS sont allé à cette bonne pâtisserie..." Pourquoi "ils" non pas "elles". Je t'assure que c'est pas Belge, est-ce que c'est arabe? Sa soeur, toute aussi arabe (mais née en Belgique) l'estime une connerie (I choose the politest word she had to say). I know that many versions of Arabic "collapse" the F and M to a common form in the plural. Is that the answer? My friend does it all the time, and it irritates the hell out of me, and his sister.

Re-reading our posts, I thought I maybe owed a little explanation (to anybody who's interested) of my relationship to Darja. On the face of it, it may seem odd that someone with an Algerian partner should be more comfortable speaking Moroccan than Algerian. To start with, his family in Belgium speak exclusively French, even when alone (like all linguists, I'm an incurable "eavesdropper"). His daughter (a school teacher of French!) is the only one who has a good grasp of Fusha, and (my impression) "looks down her nose" at Darja.

All that in Brussels, which is chock-full of Moroccans, not Algerians. With regard to the former, it would take a better analyst than I to determine whether they speak Darja heavily interlaced with French (and, bizarrely to my ear, Flemish) expressions, or French with some Darja thrown in.

I live now in Tenerife, from where I can hop on a plane and be in Morocco in less than an hour, where people are happy (and relieved) to talk to me in Darja or French, though initially we struggle on both sides with Spanish. Visiting Algeria involves a big rigmarole of visa applications, and (rightly or wrongly) I wouldn't feel safe going there without my friend or a member of his family.

Finally, but importantly, as a linguist who wants to "get it right", there are so many more resources available for learning Moroccan Darja than Algerian. I have Norbert Tapiero's "Manuel d'arabe algérien moderne", though I find it hard to believe it was "moderne" even when he wrote it, also "L'Arabe parlé algérien" by Larbi Dziri. Neither really meets my needs: Tewfik's very urban (urbane?) family would be puzzled in any language if I asked them "How is you onion crop growing this year?". Elizabeth Bergman's "Spoken Algerian Arabic" is clearly the result of solid scholarship, but presupposes a familiarity with Fusha that I don't have.

All these books are based on dialects which are spoken to the east of Oran (almost all of Algeria is to the east of Oran!). Oran is very close to the Moroccan border, and I have to wonder whether the Moroccan Darja that I already have "under my belt" might not serve me better than struggling to learn how they speak in (e.g.) Alger.

Purely anecdotal of course, but my job requires me to remember long numbers (9 or 10 digits, not phone numbers) and type them in on a phone keypad. I can remember sequences of numbers that I'm typing into the phone pad much more easily than I can remember even shorter sequences of numbers that I would have to write or say (such as unfamiliar street addresses or zip codes). I've used it to help me memorize other number sequences as well, imagining that I'm typing them into a keypad rather than saying them. I doubt this method has much history or research on it though.

That's a very interesting observation - thanks! It makes sense that that should be possible, at least, given that this exploits a different kind of memory, neither phonological nor visual. I don't know of any relevant research, but all anecdotes are gratefully received :) After all, anyone interested in the topic can test for himself whether or not this trick works for him...

Lameen, if you speak any foreign language well (I don't mean your second language, but a real proper foreign one) then you have used exactly the same "trick" as I do, and the number-memorizers do, which is to slip information which properly belongs in short-term memory into our long-term memory. I remember verbatim whole conversations I had 20 years ago, just because I learnt a new word. It's a curse.

You have paper and pencil? Write (column-wise) the word for "book" in all the languages you know, half-know, would like to know, think you ought to know.

***********

The asterisks represent the pause while you turn over the page, because you've filled it, haven't you?

People with different minds from ours can do that with numbers. No, I don't get it either, but hey, whatever...

Rowan's comment is very interesting. There have been studies of this kind of "tactile memory", as I remember in relation to keyboard and guitar players. If I can unearth specific references, I'll let you know.